CN114147419B - Design method of side rear angle surface of torus worm gear hob - Google Patents
Design method of side rear angle surface of torus worm gear hob Download PDFInfo
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Abstract
The invention discloses a design method of a side rear corner surface of a toroidal worm hob, and belongs to the field of mechanical transmission. The design method comprises the following steps: building ring surface worm gear hobAnd a left side relief surface of the at least one tooth, and comprising: rotating the rake surface of the at least one cutter tooth by a first angle θ 1 Obtaining a mapping rake face; make the left side spiral surface of the basic toroidal worm rotate by a second angle theta 2 Obtaining a left side mapping helicoid; determining a first intersecting line formed by intersecting the mapping rake face and the left side mapping spiral surface; by varying the first angle theta 1 And a second angle theta 2 Obtaining a plurality of first intersecting lines; the left side rear corner face is obtained based on a plurality of first intersecting lines. The design method realizes the design method of the side rear angle surface of the non-bladed regrindable torus worm gear hob, and ensures that the theoretical meshing area of the worm gear surface obtained by rolling and cutting the new blade edge line of the obtained cutter teeth keeps unchanged after the front cutter surface of the torus worm gear hob is regrinded, so the regrindable performance of the torus worm gear hob is realized.
Description
Technical Field
The invention relates to the field of mechanical transmission, in particular to a design method of a side rear angle surface of a ring surface worm gear hob.
Background
The worm wheel in the double-enveloping ring surface worm gear pair is formed by hobbing a ring surface worm wheel hob, and the structure of the hob influences the cutting performance, the service life, the worm wheel precision and the transmission performance of the worm gear pair. Therefore, the reasonable design and precise manufacturing of the toroidal worm gear hob are the key to obtain a high-performance toroidal worm gear pair. The torus worm hob has the characteristics of variable tooth thickness, variable tooth profile and variable helix angle. Moreover, the helical surface of the basic toric worm on which the cutting edges are located is generally an envelope surface, which makes the design and manufacture of this type of hob particularly complex.
Disclosure of Invention
The mode of designing the blade zone is a mode of designing a torus worm hob. This way, the exactness of edge line shape is guaranteed, and the strength of the cutting edge is strengthened in order to improve the single life of hobbing cutter.
Therefore, the structural form of the ring surface worm gear hob with the edge zone solves the problems of accuracy of the edge shape of the ring surface worm gear hob, difficulty in processing side rear angle surfaces, long service life and the like to a certain extent. However, the method still has the defects which need to be solved urgently. For example, the presence of the land affects the cutting performance of a torus worm gear hob. The cutting edge is a part of the spiral surface of the basic ring surface worm, and the process of hobbing the worm wheel is the enveloping process of discontinuous cutting edge, which is strictly an interference processing without local back angle, which is not beneficial to the hobbing forming of the tooth surface of the worm wheel. Moreover, the ring surface worm gear hob with the blade zone has no regrinding performance, and the whole service life and the economical efficiency of the hob are influenced. The margin only improves the single service life of the hob. Specifically, when the hob edge is damaged, the precise edge shape cannot be obtained by only regrinding the rake face, and the helical surface of the basic torus worm needs to be re-enveloped, and the rake face and the flank relief face and the like need to be re-machined. However, the remanufacturing process is complicated, which results in a less efficient overall use of the torus worm hob and increases the production costs. Therefore, it is an urgent technical problem to be solved to obtain a regrindable torus worm gear hob without theoretical blade shape errors by regrinding the rake face, and to rapidly remake the torus worm gear hob.
To address at least one of the above-identified problems and deficiencies in the prior art, embodiments of the present invention provide a method of designing a flank relief surface of an annular worm gear hob. The design method of the embodiment of the invention provides a design method of the side back angle surface of the annular worm gear hob without the blade zone. Moreover, the design method of the invention can ensure that the theoretical meshing area of the tooth surface of the worm gear obtained by rolling and cutting the new edge line of the cutter tooth remains unchanged after the front cutter surface of the torus worm gear hob is reground, thereby realizing the regrinding performance of the torus worm gear hob.
According to one aspect of the present disclosure, a method for designing a flank back corner face of a torus worm gear hob is provided, the method comprising: constructing a left side relief flank of at least one tooth of a torus worm gear hob and comprising: so thatThe rake surface of the at least one tooth is rotated by a first angle θ 1 Obtaining a mapping rake face; rotating the left flank of the basic toroid worm by a second angle theta 2 Obtaining a left side mapping helicoid; determining a first intersecting line formed by intersecting the mapping rake face and the left side mapping spiral surface; by varying the first angle theta 1 And a second angle theta 2 Obtaining a plurality of first intersecting lines; the left-side rear corner face is obtained based on a plurality of first intersecting lines.
In some embodiments, the rake surface of the at least one cutter tooth is rotated by the first angle θ 1 The rotation is clockwise around the Z axis of the basic ring surface worm; rotating the left side helicoid by the second angle theta 2 Is rotated clockwise about the Z axis.
In some embodiments, constructing the left side relief face of the at least one cutter tooth of the torus worm gear hob further comprises: and determining a second intersection line formed by the intersection of the front cutter face and the left side spiral surface, and simultaneously obtaining the left side rear angle surface based on a plurality of first intersection lines and the second intersection line.
In some embodiments, the first angle θ 1 And a second angle theta 2 Satisfies the relationship: theta 2 ＝k 1 θ 1 Wherein k is 1 Is a constant greater than 0.
In some embodiments, k is 1 In the range of 0<k 1 <0.5, first angle θ 1 In the range of 0 DEG to 30 DEG, and the first angle theta 1 The step size when selecting a plurality of values is in the range of 0.1-2 degrees.
In some embodiments, the design method further comprises: creating a right side relief flank of at least one tooth of a torus worm gear hob and comprising: rotating the right flank of the substantially toroidal worm by a third angle θ 3 Obtaining a right side mapping helicoid; determining a third intersecting line formed by intersecting the mapping rake face and the right side mapping spiral surface; by varying the first angle theta 1 And a third angle theta 3 Obtaining a plurality of third intersecting lines; and obtaining the right-side rear corner face based on a plurality of third intersecting lines.
In some embodiments, the right flank is rotated by the third angle θ 3 Is rotated counterclockwise about the Z axis.
In some embodiments, constructing the right side relief flank of the at least one tooth of the torus worm gear hob further comprises: and determining a fourth intersecting line formed by intersecting the rake face and the right helical face, and simultaneously obtaining the right rear corner face based on the plurality of third intersecting lines and the fourth intersecting line.
In some embodiments, the first angle θ 1 And a third angle theta 3 Satisfies the relationship: theta 3 ＝k 2 θ 1 Wherein k is 2 Is a constant less than 0.
In some embodiments, k is 2 In the range of-0.5<k 2 <0, first angle θ 1 In the range of 0 to 30 DEG, and the first angle theta 1 The step size when selecting multiple values is in the range of 0.1-2 deg.
Drawings
These and/or other aspects and advantages of the present invention will become apparent and readily appreciated from the following description of the preferred embodiments, taken in conjunction with the accompanying drawings of which:
FIG. 1 is a torus worm hob obtained according to an embodiment of the present invention;
FIG. 2 is a schematic view of the location of the spiral face and rake face of a basic torical worm according to an embodiment of the present invention;
FIG. 3 is a schematic illustration of the construction of a left side rear corner face according to an embodiment of the present invention;
FIG. 4A is a schematic view of a right side rear corner face construction according to an embodiment of the present invention;
fig. 4B is an enlarged view of a portion a in fig. 4A.
Detailed Description
The technical scheme of the invention is further specifically described by the following embodiments and the accompanying drawings. In the specification, the same or similar reference numerals denote the same or similar components. The following description of the embodiments of the present invention with reference to the accompanying drawings is intended to explain the general inventive concept of the present invention and should not be construed as limiting the invention.
According to the general concept of the present invention, there is provided a method of designing a flank back face of a torus worm gear hob, the method comprising: constructing a left side relief flank of at least one tooth of a torus worm gear hob and comprising: rotating the rake face of the at least one tooth by a first angle θ 1 Obtaining a mapping rake face; make the left side spiral surface of the basic toroidal worm rotate by a second angle theta 2 Obtaining a left side mapping helicoid; determining a first intersecting line formed by intersecting the mapping rake face and the left side mapping spiral surface; by varying the first angle theta 1 And a second angle theta 2 Obtaining a plurality of first intersecting lines; the left-side rear corner face is obtained based on a plurality of first intersecting lines.
The design method of the invention can obtain the annular worm gear hob without the blade zone, as shown in figure 1. The torus worm gear hob 100 comprises at least one cutter tooth 110 obtained according to the design method of the present invention. As shown in fig. 1, cutter teeth 110 do not include a land, and embodiments of the present invention change the traditional worm gear tooth surface generated by a land with a certain width into a linear edge hobbing worm gear tooth surface, which can improve the hobbing performance of a torus worm gear hob and eliminate the adverse effects of the presence of the land.
In an embodiment, when the cutting edge line (for example, the cutting edge line on the left side back corner surface) of the toroidal worm gear hob obtained according to the design method of the present invention is worn, the mapped rake surface can be reground according to the situation of wear, so as to obtain a new first intersection line (i.e., a new cutting edge line), the obtained new cutting edge lines are all located in the mapped spiral surface on the side, and the position of the basic toroidal worm spiral surface where the new cutting edge line is located along the axial direction of the hob is constant, so that the theoretical meshing area of the worm gear tooth surface which is roll-cut is ensured to be unchanged, and the invariability of the precision of the cutting edge line after regrinding of the hob is maintained. Therefore, the design method of the invention simplifies the reproduction process of the hob and prolongs the service life of the whole life cycle of the hob.
Specifically, a method of designing the side relief surfaces of the toroidal worm gear hob 100 includes constructing the left side relief surface 113 of at least one of the cutter teeth 110 of the toroidal worm gear hob 100.
In an embodiment, as shown in fig. 3, constructing a left side relief surface 113 of at least one blade tooth 110 of a torus worm gear hob 100 comprises: such that the rake surface 111 of at least one tooth 110 is rotated by a first angle θ 1 Obtaining a mapped rake surface 112; rotating the left flank 211 of the substantially toroidal worm 200 by a second angle θ 2 Obtaining a left side mapped helicoid 212; determining a first intersecting line l formed by the intersection of the mapping rake face 112 and the left side mapping spiral surface 212 1 (ii) a By varying the first angle theta 1 And a second angle theta 2 Obtain a plurality of first intersecting lines l 1 (ii) a Based on a plurality of first intersecting lines l 1 A left-side rear corner face 113 is obtained. Thus, the design method of the invention provides a design method of a girdle-free ring surface worm gear hob. When the left side back angle surface of the torus worm gear hob is worn, a new first intersection line (a new cutting edge line) can be obtained by regrinding the mapping front cutter surface so as to ensure the invariance of the precision of the regrinding back cutting edge line of the hob.
In an example, the rake surface 111 of at least one tooth 110 is rotated by a first angle θ 1 Is rotated clockwise about the Z-axis of the basic toroidal worm 200. In one example, the left helicoid 211 is rotated by a second angle θ 2 Is rotated clockwise about the Z axis. In the design process, the rake face 111 and the left flank 211 rotate around the same direction to ensure that the included angle between the designed left flank and the left basic torus worm flank is a positive value. In this case, when the worm gear tooth faces are hob-cut using the worm hob of the present invention, the left side relief faces do not interfere with the worm gear tooth faces in contact.
In one example, the first angle θ 1 And a second angle theta 2 Satisfies the relationship: theta 2 ＝k 1 θ 1 Wherein k is 1 Is a constant greater than 0. In one example, k 1 In the range of 0<k 1 <0.5, preferably k 1 In the range of 0.1 to 0.3, more preferably, k 1 In the range of 0.15 to 0.2. In one example, the first angle θ 1 In the range of 0 deg. -30 deg. (preferably 0 deg. -25 deg., more preferably 0 deg. -20 deg.), and a first angle theta 1 The step size when taking multiple values is in the range of 0.1 deg. to 2 deg. (e.g. 0.5 deg., or 1 deg.). However, it is apparent to those skilled in the art that the embodiment of the present invention is not limited thereto, and the first angle θ may be adjusted as needed 1 The value range and step length of (a).
In one example, constructing the left side relief surface 113 of the at least one blade tooth 110 of the torus worm gear hob 200 further includes: a second intersecting line l formed by the intersection of the rake face 111 and the left side spiral face 211 is determined 01 (as shown in FIG. 2), based on a plurality of first intersecting lines l 1 And the second line of intersection l 01 A left side rear corner face 113 is obtained. Second line of intersection l 01 Corresponding to theta 2 ＝θ 1 First line of intersection l when equal to 0 1 。
In one example, 10, 20, 30, 50 or more first intersecting lines l may be selected 1 To obtain the left-side rear corner face 113. First line of intersection l 1 May pass through a first angle theta 1 And a first angle theta 1 The step length when taking the value is adjusted. For example, the first angle θ may be set 1 The value is set to be 0-23 degrees, and the value is taken according to the step length of 1 degree when the value is taken, so that 24 first intersecting lines can be obtained.
In one example, the selected first plurality of lines may be fitted to smooth continuous left side trailing surface 113 by surface fitting software (e.g., Solidworks).
In one example, the left flank 113 may be constructed for each cutter tooth 110 of the torus worm gear hob 100 according to the above-described embodiment of the present invention, thereby completing the construction of each cutter tooth. In this way, when the left side rear corner face of any one of the cutter teeth of the torus worm gear hob 100 is worn, the regrinding of the torus worm gear hob 100 can be completed by regrinding the rake face 111, thereby ensuring the invariance of the regrinding back-cutting edge line accuracy of the hob.
In an embodiment, the design method of the present invention further comprises constructing a right side relief surface 114 of at least one cutter tooth 110 of the torus worm gear hob 100.
In an embodiment, as shown in fig. 4A and 4B, at least one cutter tooth 1 of a torus worm gear hob 100 is constructedThe right side rear corner face 114 of fig. 10 includes: such that right flank 213 of at least one cutter tooth 110 is rotated by a third angle theta 3 Obtaining a right side mapping helicoid 214; determining a third intersection line l formed by the intersection of the mapping rake surface 112 and the right mapping spiral surface 214 2 (ii) a By varying the first angle theta 1 And a third angle theta 3 Obtain a plurality of third intersecting lines l 2 (ii) a Based on a plurality of third intersecting lines l 2 A right side rear corner face 114 is obtained. Thus, the design method of the invention provides a design method of a girdle-free ring surface worm gear hob. When the right side back clearance surface of the torus worm gear hob needs to be reground in the later period, a new second intersection line (a new cutting edge line) can be obtained in a mode of regrinding the mapping front cutter surface, so that invariability of precision of the reground cutting edge line of the hob is ensured.
In one example, the right helicoid 213 is rotated by a third angle θ 3 Is rotated counterclockwise about the Z axis. During design, the rake face 111 and the right flank 213 are rotated in opposite directions to ensure that the right flank is designed to have a positive angle with the right base torus worm flank. In this case, when the worm gear face is hob-cut using the worm hob of the present invention, the right side relief face does not come into contact interference with the worm gear face.
In one example, the first angle θ 1 And a third angle theta 3 Satisfies the relationship: theta.theta. 3 ＝k 2 θ 1 Wherein k is 2 Is a constant less than 0. In one example, k 2 In the range of-0.5<k 2 <0, preferably k 2 In the range of-0.3 to-0.1, more preferably, k 2 In the range of-0.2 to-0.15. In one example, the first angle θ 1 In the range of 0 deg. -30 deg. (preferably 0 deg. -25 deg., more preferably 0 deg. -20 deg.), and the first angle theta 1 The step size when taking multiple values is in the range of 0.1 deg. -2 deg. (e.g. 0.5 deg., or 1 deg.). However, it is apparent to those skilled in the art that the embodiment of the present invention is not limited thereto, and the first angle θ may be adjusted as needed 1 The value range and step length of (c).
In one example, a torus worm gear hob 200 is built upThe right side relief flank 114 of the at least one cutter tooth 110 further comprises: a fourth intersecting line l formed by the intersection of the rake face 111 and the right flank 213 is determined 02 (as shown in FIG. 2) based on a plurality of third intersecting lines l 2 And a fourth line of intersection l 02 A right side rear corner face 114 is obtained. Fourth line of intersection l 02 Corresponding to theta 2 ＝θ 1 Third line of intersection l when equal to 0 2 。
In one example, 10, 20, 30, 50 or more third intersecting lines l may be selected 2 To obtain the right-side rear corner face 114. Third line of intersection l 2 May pass through a first angle theta 1 And the first angle theta 1 The step length when taking the value is adjusted. For example, the first angle θ may be set 1 The value is set to be 0-23 degrees, and the value is taken according to the step length of 1 degree when the value is taken, so that 24 third intersecting lines can be obtained.
In one example, the selected third plurality of intersecting lines l may be fitted by surface fitting software (e.g., Solidworks) 2 Fitting into a smooth continuous right side relief surface 114.
In one example, the right flank 114 may be constructed for each cutter tooth 110 of the torus worm gear hob 100 in accordance with the above-described embodiments of the present invention, thereby completing the design of each cutter tooth. In this way, when the right side rear corner surface of any one of the cutter teeth of the toroidal worm gear hob 100 is worn, the regrinding of the toroidal worm gear hob 100 can be completed by regrinding the front cutter surface 111, thereby ensuring the invariance of the precision of the regrinding back cutting edge line of the hob.
The following merely illustrates a portion of an embodiment of the present invention, which is intended to be illustrative only; still other possible embodiments of the invention will be apparent to those skilled in the art and will not be described in detail herein.
Taking a double-conical surface enveloping ring surface worm gear hob as an example, the basic parameters are as follows: center distance a is 260mm, and transmission ratio i 12 8, right-handed worm, number of heads Z 1 Radius of addendum arc R5 a 193mm root radius of arc f 214mm, 135mm and 5 rows of cutter teeth.
As shown in fig. 2, a substantially toroidal voluteThe rod 200 comprises a left helical surface 211 and a right helical surface 213, wherein the left helical surface 211 intersects with the rake face 111 to form a second intersection line l 01 The right spiral surface 213 intersects with the rake surface 111 to form a fourth intersection line l 02 The Z-axis of the basic toroidal worm 200 coincides with the axis of revolution of the basic toroidal worm 200 and is in a positive direction to the right.
The rake face 111 is rotated clockwise about the Z axis by a first angle theta 1 The mapped rake surface 112 is obtained while rotating the left flank 211 clockwise about the Z-axis by a second angle θ 2 Obtaining a left side mapping spiral surface 212, and the mapping rake surface 112 and the left side mapping spiral surface 212 are intersected to form a first intersection line l 1 . Let theta 2 ＝k 1 θ 1 Take k 1 0.18, make θ 1 The value is taken according to the step length of 1 degree within the range of 0 degree to 23 degrees to obtain the corresponding theta 2 The value is obtained. Each group theta 1 And theta 2 The value corresponds to a first intersection line l 1 By varying θ 1 And theta 2 The total of 24 first intersecting lines l are obtained 1 Wherein when theta 1 ＝θ 2 When equal to 0 DEG, corresponds to a second intersection line l 01 . The 24 first intersecting lines l are fitted by surface fitting software such as Solidworks 1 Fitting into a smooth continuous hob tooth left flank back flank 113.
Rotate the right side spiral surface 213 counterclockwise around the Z axis by a third angle theta 3 The right side mapping spiral surface 214 is obtained, and the mapping rake face 112 and the right side mapping spiral surface 214 intersect to form a third intersecting line l 2 . Let theta 3 ＝k 2 θ 1 Get k 2 When the ratio is-0.18, in the same manner, let θ 1 Taking 24 values in 1 degree step in the range of 0 to 23 degrees to obtain corresponding third angle theta 3 The value is obtained. Each group theta 1 And theta 3 The value corresponds to a third intersection line l 2 By varying theta 1 And theta 3 The value of (c) is obtained for a total of 24 third intersecting lines l 2 Wherein when theta 1 ＝θ 3 When the angle is 0 DEG, the angle corresponds to the fourth intersection line l 02 . The 24 third intersecting lines l are fitted by surface fitting software such as Solidworks 2 Fitting into a smooth continuous right flank relief 114 of the hob teeth.
According to the method for constructing the left back angle surface and the right back angle surface of the cutter teeth, the left back angle surface and the right back angle surface of each cutter tooth of the torus worm gear hob are constructed one by one, and the torus worm gear hob 100 without the cutting edge is obtained (as shown in fig. 1). When the cutting edge line of the torus worm gear hob 100 according to the embodiment of the present invention is worn, the mapping rake face 112 may be reground, and the new cutting edge line is a new first intersection line and a new third intersection line, so that the obtained new cutting edge lines are all located on the mapping helicoids of the corresponding sides, thereby ensuring that the theoretical meshing area of the worm gear tooth face which is roll-cut is not changed.
Although a few embodiments of the present general inventive concept have been shown and described, it will be appreciated by those skilled in the art that changes may be made in these embodiments without departing from the principles and spirit of the general inventive concept, the scope of which is defined in the appended claims and their equivalents.
Claims (6)
1. A method for designing a side rear corner surface of a toroidal worm gear hob, the method comprising:
constructing a left side relief flank of at least one tooth of a torus worm gear hob and comprising:
with the rake face of said at least one tooth being about a substantially toroidal wormZThe shaft rotates clockwise by a first angleθ 1 Obtaining a mapping rake face;
so that the left flank of the basic toroid worm winds around saidZThe shaft rotates clockwise by a second angleθ 2 Obtaining a left side mapping helicoid;
determining a first intersecting line formed by intersecting the mapping rake face and the left side mapping spiral surface;
by varying the first angleθ 1 And a second angleθ 2 Obtaining a plurality of first intersecting lines;
determining a second intersecting line formed by the intersection of the rake face and the left spiral surface;
the left-side rear corner face is obtained based on a plurality of first intersecting lines and second intersecting lines,
wherein the first angleθ 1 And a second angleθ 2 The following relation is satisfied:θ 2 = k 1 θ 1 whereink 1 Is a constant number greater than 0 and is,k 1 in the range of 0< k 1 < 0.5，
First angleθ 1 In the range of 0 DEG to 30 DEG, and a first angleθ 1 The step size when selecting multiple values is within the range of 0.1-2 degrees.
2. The design method of claim 1, further comprising:
creating a right side relief flank of at least one tooth of a torus worm gear hob and comprising:
rotating the right flank of the substantially toroidal worm by a third angleθ 3 Obtaining a right side mapping helicoid;
determining a third intersecting line formed by intersecting the mapping rake face and the right side mapping spiral surface;
by varying the first angleθ 1 And a third angleθ 3 Obtaining a plurality of third intersecting lines;
and obtaining the right-side rear corner face based on a plurality of third intersecting lines.
3. The design method according to claim 2,
rotating the right flank by the third angleθ 3 Is wound around theZThe shaft rotates counterclockwise.
4. The design method according to claim 3,
constructing the right side relief flank of at least one tooth of a torus worm gear hob further comprises:
determining a fourth intersecting line formed by the intersection of the rake face and the right helical face,
and obtaining the right-side rear corner face based on a plurality of third intersecting lines and the fourth intersecting lines.
5. The design method according to claim 3,
the first angleθ 1 And a third angleθ 3 Satisfies the relationship:θ 3 = k 2 θ 1 in whichk 2 Is a constant less than 0.
6. The design method according to claim 5,
k 2 in the range of-0.5< k 2 < 0，
First angleθ 1 In the range of 0 DEG to 30 DEG, and a first angleθ 1 The step size when selecting multiple values is within the range of 0.1-2 degrees.
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Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US1430485A (en) * | 1921-01-28 | 1922-09-26 | Gould & Eberhardt | Hob and method of making it |
| CN103223533A (en) * | 2013-05-10 | 2013-07-31 | 中国农业大学 | Method for designing side rear angle surfaces of double-enveloping ring surface worm gear hob |
| CN104440419A (en) * | 2014-11-04 | 2015-03-25 | 中国农业大学 | Numerical control grinding method for planar double-enveloping ring surface worm gear hob rear side edged surfaces |
| CN106956171A (en) * | 2017-04-05 | 2017-07-18 | 中国农业大学 | The numerical control grinding method of Double-conical-surface twice-enveloping enveloping worm hob side relief |
| CN107322059A (en) * | 2017-07-05 | 2017-11-07 | 中国农业大学 | Enveloping worm hob CAD/CAM approach based on universal numerical control milling machine |
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Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US1430485A (en) * | 1921-01-28 | 1922-09-26 | Gould & Eberhardt | Hob and method of making it |
| CN103223533A (en) * | 2013-05-10 | 2013-07-31 | 中国农业大学 | Method for designing side rear angle surfaces of double-enveloping ring surface worm gear hob |
| CN104440419A (en) * | 2014-11-04 | 2015-03-25 | 中国农业大学 | Numerical control grinding method for planar double-enveloping ring surface worm gear hob rear side edged surfaces |
| CN106956171A (en) * | 2017-04-05 | 2017-07-18 | 中国农业大学 | The numerical control grinding method of Double-conical-surface twice-enveloping enveloping worm hob side relief |
| CN107322059A (en) * | 2017-07-05 | 2017-11-07 | 中国农业大学 | Enveloping worm hob CAD/CAM approach based on universal numerical control milling machine |
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